Question

determine o valor de b-a

Answer 1

Lembre-se que: $\sqrt[b]{a^c} =a^{\frac{c}{b}}$

$\sqrt[a]{ \sqrt{2} }=\sqrt[12]{ \sqrt{2} }\\\\\sqrt[a]{2^{\frac{1}{2}}}=2^{\frac{1}{12}}\\\\2^{\frac{1}{2a}}=2^{\frac{1}{12}}\\\\\frac{1}{2a}=\frac{1}{12}\\\\2a=12\\\\a=6\\\\\\\sqrt[b]{ \sqrt[3]{3} }=\sqrt[15]{ \sqrt{3} }\\\\\sqrt[b]{3^{\frac{1}{3}}}=3^{\frac{1}{15}}\\\\3^{\frac{1}{3b}}=3^{\frac{1}{15}}\\\\\frac{1}{3b}=\frac{1}{15}\\\\3b=15\\\\b=5$

b - a = 5 - 6 = -1